Nonexistence of solutions of the p-adic strings

摘要

We discuss mathematical aspects of the nonexistence of continuous (nontrivial) solutions of boundary value problems for equations of p-adic closed and open strings in the one-dimensional case. We find that the number of sign changes of the solution ψ(t) is not equal to the order of zeros of the function ψ~n(t) and that nonnegative (nonpositive) solutions do not exist. In the case of even n, if a solution ψ exists, then the orders of zeros of the function ψn and the order of its tangency to positive maximums (minimums) are not divisible by four and therefore have the form 2(2r + 1), r ≥ 0.